Optimization problems involving matrix multiplication with applications in materials science and biology

Optimization problems are considered that involve the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and materials science among others, and are known to be NP-hard for a special case of interest. The underlying structure of such optimization problems is analysed for two particular applications and, depending on the matrix family, compact-size mixed-integer linear or quadratically constrained quadratic programming reformulations are obtained that can be solved via commercial solvers. Finally, the results are presented of computational experiments that demonstrate the success of the author's approach compared to heuristic and enumeration methods predominant in the literature